Let W be the number of failures until the first success; that is, W = T-1. Show that W has mean (1-pi)/pi and variance (1-pi)/(pi^2).
I know for mean, E(T) = 1/pi and for variance Var(T) = (1-pi)/(pi^2).
I guess I'm looking for E(T(W)) = E(T(T-1)) and Var(T(W)) = Var(T(T-1)).
I've included how I've started so far in the attachment. Note I messed up on the last part in the step where I moved pi in front of summation. Should say (t-1). Sorry.
Can someone help me with this proof.